The Collaborative International Dictionary of English v.0.48:

Competence \Com"pe*tence\, Competency \Com"pe*ten*cy\, n. [Cf.
   F. comp['e]tence, from L. competentia agreement.]
   1. The state of being competent; fitness; ability; adequacy;
      power.
      [1913 Webster]

            The loan demonstrates, in regard to instrumental
            resources, the competency of this kingdom to the
            assertion of the common cause.        --Burke.
      [1913 Webster]

            To make them act zealously is not in the competence
            of law.                               --Burke.
      [1913 Webster]

   2. Property or means sufficient for the necessaries and
      conveniences of life; sufficiency without excess.
      [1913 Webster]

            Reason's whole pleasure, all the joys of sense,
            Lie in three words -- health, peace, and competence.
                                                  --Pope.
      [1913 Webster]

            Superfluity comes sooner by white hairs, but
            competency lives longer.              --Shak.
      [1913 Webster]

   3. (Law)
      (a) Legal capacity or qualifications; fitness; as, the
          competency of a witness or of a evidence.
      (b) Right or authority; legal power or capacity to take
          cognizance of a cause; as, the competence of a judge
          or court. --Kent.
          [1913 Webster]

   5. the quality of being adequately or well qualified
      physically and intellectually, especially possession of
      the skill and knowledge required (for a task).
      [WordNet 1.5 +PJC]

WordNet (r) 3.0 (2006):

competency
    n 1: the quality of being adequately or well qualified
         physically and intellectually [syn: competence,
         competency] [ant: incompetence, incompetency]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

COMPETENCY, evidence. The legal fitness or ability of a witness to be heard
on the trial of a cause. This term is also applied to written or other
evidence which may be legally given on such trial, as, depositions, letters,
account-books, and the like.
     2. Prima facie every person offered is a competent witness, and must be
received, unless Lis incompetency (q.v.) appears. 9 State Tr. 652.
     3. There is a difference between competency and credibility. A witness
may be competent, and, on examination, his story may be so contradictory and
improbable that he may not be believed; on the contrary he may be
incompetent, and yet be perfectly credible if he were examined.
     4. The court are the sole judges of the competency of a witness, and
may, for the purpose of deciding whether the witness is or is not competent,
ascertain all the facts necessary to form a judgment. Vide 8 Watts, R. 227;
and articles Credibility; Incompetency; Interest; Witness.
     5. In the French law, by competency is understood the right in a court
to exercise jurisdiction in a particular case; as, where the, law gives
jurisdiction to the court when a thousand francs shall be in dispute, the
court is competent if, the sum demanded is a thousand francs or upwards,
although the plaintiff may ultimately recover less.